There are a lot of ways to clean a rifle. Courtesy of ODCMP, SSG William T. Pace of the US Army's Maksmanship Unit gives us his method. I've used a similar method before and it does work just fine.
Since I changed to Eezox as my primary cleaner/lube, I've developed a different method that seems to work quite well. I am going to investigate his greater use of the brush to see if it might help get me off the cleaning bench faster. I figure that if they don't worry about using a brush in a match barrel that much, I ought to be just fine in my standard barrels.